Introduction To The Mathematics Of Operations Research With Mathematica
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Introduction to the Mathematics of Operations Research with Mathematica®
The breadth of information about operations research and the overwhelming size of previous sources on the subject make it a difficult topic for non-specialists to grasp. Fortunately, Introduction to the Mathematics of Operations Research with Mathematica®, Second Edition delivers a concise analysis that benefits professionals in operations research and related fields in statistics, management, applied mathematics, and finance. The second edition retains the character of the earlier version, while incorporating developments in the sphere of operations research, technology, and mathematics pedagogy. Covering the topics crucial to applied mathematics, it examines graph theory, linear programming, stochastic processes, and dynamic programming. This self-contained text includes an accompanying electronic version and a package of useful commands. The electronic version is in the form of Mathematica notebooks, enabling you to devise, edit, and execute/reexecute commands, increasing your level of comprehension and problem-solving. Mathematica sharpens the impact of this book by allowing you to conveniently carry out graph algorithms, experiment with large powers of adjacency matrices in order to check the path counting theorem and Markov chains, construct feasible regions of linear programming problems, and use the "dictionary" method to solve these problems. You can also create simulators for Markov chains, Poisson processes, and Brownian motions in Mathematica, increasing your understanding of the defining conditions of these processes. Among many other benefits, Mathematica also promotes recursive solutions for problems related to first passage times and absorption probabilities.
Introduction to the Mathematics of Operations Research with Mathematica®, Second Edition
Nice text for advanced undergraduates and beginning graduate students provides review, from the viewpoint of operations research and its (diverse) applications, of graph theory, linear programming, stochastic processes and dynamic programming, and of related material. The seven chapters are punctu
Financial Mathematics
Financial Mathematics: From Discrete to Continuous Time is a study of the mathematical ideas and techniques that are important to the two main arms of the area of financial mathematics: portfolio optimization and derivative valuation. The text is authored for courses taken by advanced undergraduates, MBA, or other students in quantitative finance programs. The approach will be mathematically correct but informal, sometimes omitting proofs of the more difficult results and stressing practical results and interpretation. The text will not be dependent on any particular technology, but it will be laced with examples requiring the numerical and graphical power of the machine. The text illustrates simulation techniques to stand in for analytical techniques when the latter are impractical. There will be an electronic version of the text that integrates Mathematica functionality into the development, making full use of the computational and simulation tools that this program provides. Prerequisites are good courses in mathematical probability, acquaintance with statistical estimation, and a grounding in matrix algebra. The highlights of the text are: A thorough presentation of the problem of portfolio optimization, leading in a natural way to the Capital Market Theory Dynamic programming and the optimal portfolio selection-consumption problem through time An intuitive approach to Brownian motion and stochastic integral models for continuous time problems The Black-Scholes equation for simple European option values, derived in several different ways A chapter on several types of exotic options Material on the management of risk in several contexts